Technically, depreciation is an accounting term.
The IRS equivalent that gives you tax deductions is called cost recovery. You will need to know both terms if you are doing Internet research. In common speech, though, everyone just calls both of them depreciation.
Depreciation deductions are available to investors, not to homeowners.
Depreciation is an agreed-upon fiction that your real estate improvements (not the land itself, but everything else) are becoming less valuable every year at a steady rate. The IRS is of the opinion that residential rental properties will last for 27.5 years after you buy or build them and then be worthless.
The IRS allows you to pretend that commercial properties will last for 39 years, and convenience stores will have no value after 15 years. As a result, you are allowed to write off, as a deduction, the pro rata amount that the property loses in value each year.
You can increase your deductions if you take advantage of something called cost allocation depreciation. With this, some components of your property improvements can be split out and depreciated more quickly than the whole. Carpets, exterior lighting, fencing, security systems, and other items can be depreciated over five, seven, or fifteen years, for example.
Talk to an accountant or do a good bit of research before taking this route, however. Guessing can result in audits, fines, and penalties.